LOW-REGULARITY INTEGRATORS FOR NONLINEAR DIRAC EQUATIONS

作者：Schratz, Katharina^*; Wang, Yan; Zhao, Xiaofei

来源：Mathematics of Computation, 2021, 90(327): 189-214.

DOI：10.1090/mcom/3557

• Nonlinear Dirac equation
• Dirac-Poisson system
• exponential-type integrator
• low regularity
• optimal convergence
• splitting schemes

In this work, we consider the numerical integration of the nonlinear Dirac equation and the Dirac-Poisson system (NDEs) under rough initial data. We propose an ultra low-regularity integrator (ULI) for solving the NDEs which enables optimal first-order time convergence in H-r for solutions in H-r, i.e., without requiring any additional regularity on the solution. In contrast to classical methods, a ULI overcomes the numerical loss of derivatives and is therefore more efficient and accurate for approximating low regular solutions. Convergence theorems and the extension of a ULI to second order are established. Numerical experiments confirm the theoretical results and underline the favourable error behaviour of the new method at low regularity compared to classical integration schemes.

• 单位
  武汉大学